reserve V for RealLinearSpace;
reserve p,q,r,u,v,w,y,u1,v1,w1 for Element of V;
reserve a,b,c,d,a1,b1,c1,a2,b2,c2,a3,b3,e,f for Real;

theorem Th12:
  not u,v,w are_LinDep implies u is not zero & v is not zero & w
  is not zero & not are_Prop u,v & not are_Prop v,w & not are_Prop w,u
by Th10,Th11;
